Mean Deviation

TL;DR

Quantifies how far, on average, data points are from the mean.
Computed by averaging the absolute differences between each value and the mean.
Useful for gauging typical deviation without squaring differences.

Definition

Mean deviation is a statistical measure used to describe the dispersion of a dataset. It is calculated by taking the absolute difference between each data point and the mean of the data, then averaging those differences.

$\text{Mean Deviation} = \frac{1}{n}\sum_{i=1}^{n} \left|x_i - \bar{x}\right|$

Explanation

To compute mean deviation:

Find the mean (average) of the dataset.
For each data point, compute the absolute difference from the mean.
Average those absolute differences to obtain the mean deviation.

This result expresses, in the same units as the data, how far data points are from the mean on average.

Examples

Simple numeric dataset

Given a dataset of 5 numbers: 1, 2, 3, 4, and 5. The mean is 3. The absolute differences from the mean are:

|1 - 3| = 2
|2 - 3| = 1
|3 - 3| = 0
|4 - 3| = 1
|5 - 3| = 2

The average of these differences is 1.2, so the mean deviation is 1.2.

Stock prices

If a dataset of stock prices has a mean price of $100 and the mean deviation is$ 10, that indicates the stock prices typically fluctuate by $10 from the mean.

Use cases

Understanding the dispersion of a dataset.
Supporting predictions or decisions by conveying how much values typically vary from the mean.

Mean
Dispersion